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Revisiting Exhaustivity and Specificity Using Propositional Logic and Lattice Theory

Karam Abdulahhad, Jean-Pierre Chevallet, Catherine Berrut
2013 Proceedings of the 2013 Conference on the Theory of Information Retrieval - ICTIR '13  
We use propositional logic and lattice theory in order to redefine the two implications and their uncertainty P (d → q) and P (q → d).  ...  Exhaustivity and Specificity in logical Information Retrieval framework were introduced by Nie [16].  ...  We redefine Exhaustivity and Specificity using Propositional Logic and Lattice theory, and we theoretically integrate them into IR models, in Section 3.  ... 
doi:10.1145/2499178.2499187 dblp:conf/ictir/AbdulahhadCB13 fatcat:vdxgkvcacrcnlpvmrdb7kvuvxu

A Lattice-Based Approach to Computing Warranted Beliefs in Skeptical Argumentation Frameworks

Carlos Iván Chesñevar, Guillermo Ricardo Simari
2007 International Joint Conference on Artificial Intelligence  
We show that such search space can be defined as a lattice, and illustrate how the so-called dialectical constraints can play a role for guiding the efficient computation of warranted arguments.  ...  This research was partially supported by the Dept. of Computer Science and Eng., SeCyT, U.N.Sur, CONICET, and ANPCyT (PICT 13096, 15043, PAV076), Argentina.  ...  Partial research support was also obtained from Project TIN2004-07933-C03-01/03 and Ramón y Cajal Program (MCyT, Spain).  ... 
dblp:conf/ijcai/ChesnevarS07 fatcat:o7d3kqadwnhtdluipvqyd3wxsa

Computational Complexity of Deciding Provability in Linear Logic and its Fragments [article]

Florian Chudigiewitsch
2021 arXiv   pre-print
Linear logic has, for example, found applications in proof theory, quantum logic, and the theory of programming languages.  ...  This interpretation makes linear logic a useful tool for formalisation in mathematics and computer science.  ...  For this, we propose a lattice of fragments of linear logic, inspired by Post's lattice for propositional logic [ ].  ... 
arXiv:2110.00562v1 fatcat:a6sidawnbjh5jpf2cvrermfrcy

Logic Column 18: Alternative Logics: A Book Review [article]

Riccardo Pucella
2007 arXiv   pre-print
This article discusses two books on the topic of alternative logics in science: "Deviant Logic", by Susan Haack, and "Alternative Logics: Do Sciences Need Them?", edited by Paul Weingartner.  ...  Here are some (by no means disjoint or exhaustive) categories we can readily identify: • Specification and verification: The problem of specifying and formally verifying properties of systems is central  ...  Specification are often expressed in a form of modal logic, and verified by model checking: the logic serves as a formal language for writing down specifications, and verification amounts to checking that  ... 
arXiv:0705.1367v1 fatcat:sehpdwjpwvbepakwz65tkzokze

The Circus Testing Theory Revisited in Isabelle/HOL [chapter]

Abderrahmane Feliachi, Marie-Claude Gaudel, Makarius Wenzel, Burkhart Wolff
2013 Lecture Notes in Computer Science  
Based on this formal representation of the semantics we revisit the original associated testing theory. We discovered unforeseen simplifications in both definitions and symbolic computations.  ...  The approach lends itself to the construction of a tool, that directly uses semantic definitions of the language as well as derived rules of its testing theory, and thus provides some powerful symbolic  ...  Isabelle/HOL uses this specification to define the relation as least fixed-point on the lattice of powersets (according to Knaster-Tarski).  ... 
doi:10.1007/978-3-642-41202-8_10 fatcat:ubmaipwzuje2vcf67myeb7ph3y

A General Theory of Concept Lattice (I): Emergence of General Concept Lattice [article]

Tsong-Ming Liaw, Simon C. Lin
2019 arXiv   pre-print
It will be shown that one can always regain the formal concept lattice and rough set lattice from the general concept lattice.  ...  As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties  ...  One may construct the GCL in terms of lattice theory [1, 10, 12] . Proposition 3.16.  ... 
arXiv:1908.01056v1 fatcat:dqbldxlvdbcnfdvnjc2xn5bew4

Quantum Logical Structures For Identical Particles [article]

Federico Holik, Decio Krause, Ignacio Gómez
2013 arXiv   pre-print
In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16].  ...  In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosoph-ical implications.  ...  The standard quantum logical approach to QM [10, 11, 30, 43, 8, 12, 27] , uses the lattice of projections of the Hilbert space of the system as the lattice of propositions (see Section 3) .  ... 
arXiv:1305.5242v1 fatcat:ccqg5l6k65fqjpcaeqvmtlm7gy

Using SPARQL to Test for Lattices: Application to Quality Assurance in Biomedical Ontologies [chapter]

Guo-Qiang Zhang, Olivier Bodenreider
2010 Lecture Notes in Computer Science  
Our experimental results have been groundbreaking: for the first time, all non-lattice pairs in SNOMED CT have been identified exhaustively from 34 million candidate pairs using over 2.5 billion queries  ...  RDF, SPARQL and related tooling provide an eAEcient platform for implementing lattice algorithms on large data structures.  ...  Acknowledgements This research was supported in part by the Intramural Research Program of the National Library of Medicine (NLM), and in part by Clinical and Translational Science Award (UL1 RR024989)  ... 
doi:10.1007/978-3-642-17749-1_18 pmid:25699294 pmcid:PMC4330995 fatcat:srdrq2xsmff53bgw3cmugzbyxe

Relevant Logic and Paraconsistency [chapter]

John Slaney
2005 Lecture Notes in Computer Science  
The relevant refusal to validate these inferences is defended, and finally it is suggested that more needs to be done towards a satisfactory theory of when they may nonetheless safely be used.  ...  The relationship between relevant logic and resolution, and especially the disjunctive syllogism, is then examined.  ...  Suppose that truth and falsehood are neither collectively exhaustive nor mutually exclusive, but rather are treated in the formal semantics of logic as two independent properties that propositions may  ... 
doi:10.1007/978-3-540-30597-2_9 fatcat:552ct22xdbahzkksi4c67tnkhe

A method for rigorous design of reconfigurable systems

Alexandre Madeira, Renato Neves, Luís S. Barbosa, Manuel A. Martins
2016 Science of Computer Programming  
The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic  ...  This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation  ...  Examples range from classical logics (propositional, equational, first order, etc.), to the ones underlying specification and programming languages or used for describing particular systems from different  ... 
doi:10.1016/j.scico.2016.05.001 fatcat:eqtbwavwqfgihmcyuls3vq73oy

An Algebraic Glimpse at Bunched Implications and Separation Logic [article]

Peter Jipsen, Tadeusz Litak
2018 arXiv   pre-print
We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics.  ...  After briefly discussing the lattice of subvarieties of GBI, we present a suitable duality for GBI along the lines of Esakia and Priestley and an algebraic proof of cut elimination in the setting of residuated  ...  other things would not have happened; Nick Galatos and Kazushige Terui for suggesting the idea to write this overview, and for their patience and support during the very long write-up period; Nick, Peter  ... 
arXiv:1709.07063v2 fatcat:mo56tyegqned5htws2wazhpphu

Topological duality for distributive lattices, and applications [article]

Mai Gehrke, Sam van Gool
2022 arXiv   pre-print
: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata.  ...  This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science.  ...  : semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata.  ... 
arXiv:2203.03286v2 fatcat:bs6pfodmkfgnhpegiuvcymb3fy

Truth versus information in logic programming

LEE NAISH, HARALD SØNDERGAARD
2013 Theory and Practice of Logic Programming  
This allows us to shed new light on many aspects of logic programming, including program analysis, type and mode systems, declarative debugging and the relationships between specifications and programs  ...  In this paper we suggest that the additional truth values of Fitting/Kunen and Naish are best viewed as duals. We use Belnap's four-valued logic (Belnap, N. D. 1977. A useful four-valued logic.  ...  Two-valued semantics There are three aspects to the semantics of logic programs: proof theory, model theory and fixed point theory (see Lloyd (1984) , for example).  ... 
doi:10.1017/s1471068413000069 fatcat:iud5qwdojrdqvl6qiu45pl5oym

Formal Concept Analysis and Information Retrieval – A Survey [chapter]

Victor Codocedo, Amedeo Napoli
2015 Lecture Notes in Computer Science  
Currently, FCA theory supports dozens of different retrieval applications, ranging from traditional document indices to file systems, recommendation, multi-media and more recently, semantic linked data  ...  In this paper we present a comprehensive study on how FCA has been used to support IR systems.  ...  How have FCA and concept lattices been used in the context of IR applications?  ... 
doi:10.1007/978-3-319-19545-2_4 fatcat:ibbabj5khbecrj3zgvmalpb6ja

Logic for physical space

Marco Aiello, Guram Bezhanishvili, Isabelle Bloch, Valentin Goranko
2011 Synthese  
From the initial axiomatic efforts of Euclid, we revisit the major milestones in the logical representation of space and investigate current trends.  ...  This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space.  ...  Acknowledgements We thank Elisabetta Pallante for fruitful discussion on the theory of quantum gravity and de Sitter space-time.  ... 
doi:10.1007/s11229-011-9913-9 fatcat:agtphwjsufexvpxrwbpzkqjotq
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